@Article{IJNAM-18-740,
author = {Elvetun , Ole Iøseth and Nielsen , Bjørn Fredrik},
title = {Modified Tikhonov Regularization for Identifying Several Sources},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2021},
volume = {18},
number = {6},
pages = {740--757},
abstract = {<p style="text-align: justify;">We study whether a modified version of Tikhonov regularization can be used to identify
several local sources from Dirichlet boundary data for a prototypical elliptic PDE. This paper
extends the results presented in [5]. It turns out that the possibility of distinguishing between
two, or more, sources depends on the smoothing properties of a second or fourth order PDE.
Consequently, the geometry of the involved domain, as well as the position of the sources relative
to the boundary of this domain, determines the identifiability. We also present a uniqueness
result for the identification of a single local source. This result is derived in terms of an abstract
operator framework and is therefore not only applicable to the model problem studied in this
paper. Our schemes yield quadratic optimization problems and can thus be solved with standard
software tools. In addition to a theoretical investigation, this paper also contains several numerical
experiments.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/19948.html}
}